A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{{{x^3}}}{6}$ If the coefficient of friction is $0.5$,the maximum height above the ground at which the block can be placed without slipping is:
A block is projected with speed $20 \,m / s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in figure. The speed of body at the end of $4$ second will be ............ $m / s$ ( $g=$ $10 \,m / s ^2$ )
A bag is gently dropped on a conveyor belt moving at a speed of $2\,m / s$. The coefficient of friction between the conveyor belt and bag is $0.4$ Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is $.....m$ [Take $g=10\,m / s ^{-2}$ ]
Put a uniform meter scale horizontally on your extended index fingers with the left one at $0.00 cm$ and the right one at $90.00 cm$. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_R$ from the center ( $50.00 cm$ ) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are $0.40$ and $0.32$ , respectively, the value of $x_R($ in $cm )$ is. . . . . . .